Using Computer Simulations to Help Understand Flow
Statistics and Structures at the Air-Ocean Interface
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Shen, Lian, and Dick Yue. “Using Computer Simulations to Help
Understand Flow Statistics and Structures at the Air-Ocean
Interface.” Oceanography 19.1 (2006): 52–63. Copyright 2006 by
The Oceanography Society
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http://dx.doi.org/10.5670/oceanog.2006.90
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USING COMPUTER SIMULATIONS TO HELP
UNDERSTAND FLOW STATISTICS AND STRUCTURES
AIROCEAN
INTERFACE
AT THE
B Y L I A N S H E N A N D D I C K K . P. Y U E
The interaction among atmosphere, oceans, and surface waves
is an important process with many oceanographic and environmental applications. It directly affects the motion and fate of
pollutants such as oil spills. The oceans have an enormous capacity for mass and heat storage. The air-sea exchange of heat,
humidity, momentum, and greenhouse gases directly affects
short-term weather evolutions and long-term climate changes.
In addition, the accurate prediction of air-sea interaction is of
vital importance to many of the Navy’s applications, including
the operation of naval surface ships and remote sensing.
From the viewpoint of basic science, air-sea interaction is
a challenging fluid-mechanics problem involving turbulence,
waves, multiphase flows, and mixing, all of which operate at
multiple temporal and spatial scales. The controlling transfer
processes are the wind, ocean surface current, wave, and wavebreaking, all of which involve atmospheric and ocean flows in
the vicinity of an air-water interface. Considerable work has
been done to understand aspects of this problem in terms of
simplified theory. Nevertheless, due to the complex nature of
the physical problem, our current understanding of the mechanisms for the transport of mass, momentum, and heat within
the atmosphere-ocean wave boundary layer is quite limited.
In particular, the essential dynamics of the coupled air-sea
boundary layers at small scales (say, from millimeters to tens of
meters) remain elusive. As a result, existing theories and predic-
52
Oceanography
Vol. 19, No. 1, Mar. 2006
tion tools have to rely on empirical parameterization. There is
a critical need for a detailed study of the small-scale physics at
the air-water interface, which is a foundation for the development of large-scale simulation and prediction tools.
In recent years, we have been using high-performance computers with powerful simulation capabilities as a research tool
to investigate the mechanisms of air-sea interactions at small
scales. In direct simulations, the governing equations for the
coupled flow are solved numerically, typically with a fine computational grid. Even with very large computers, many of the
underlying physical processes, generally associated with the
turbulent nature of the flow, are not resolved. To allow the
problem to be solved, or “closed,” the numerical simulations
require “closure models,” which in effect express the unknown
and non-resolved quantities in terms of those that are known
or resolved in the simulation. Such closure models aim to capture the underlying physical mechanisms and are typically expressed in terms of variables or parameters describing the overall problem. These parameterizations are usually guided by finer-resolution direct simulations that do not contain the closure
models. The purpose of our numerical study is to complement
field and laboratory measurement and theoretical investigation.
With collaboration among different disciplines, we hope to obtain improved physical understanding and parameterization of
air-sea interactions.
This article has been published in Oceanography, Volume 19, Number 1, a quarterly journal of The Oceanography Society. Copyright 2006 by The Oceanography Society. All rights reserved. Permission is granted to copy this article for use in teaching and research. Republication, systemmatic reproduction,
or collective redistirbution of any portion of this article by photocopy machine, reposting, or other means is permitted only with the approval of The Oceanography Society. Send all correspondence to: info@tos.org or Th e Oceanography Society, PO Box 1931, Rockville, MD 20849-1931, USA.
A D V A N C E S I N C O M P U TAT I O N A L O C E A N O G R A P H Y
...we have been using high-performance
computers with powerful simulation
capabilities as a research tool to investigate
the mechanisms of air-sea interactions
at small scales.
Oceanography
Vol. 19, No. 1, Mar. 2006
53
In our study, the basic equations
governing the conservation of mass
and momentum of the air and water
turbulent flows, namely the continuity
equation and the Navier-Stokes equations, are solved numerically. An inherent challenge in turbulence simulation
is the requirement to capture the effects
of all the flow structures, often referred
To augment DNS and to extend the
results to larger-scale problems, we use
a second approach called large-eddy
simulation (LES). In LES, only the large
eddies are simulated directly while the
effects of small eddies (smaller than
the numerical grid scales) are modeled.
With high-performance computing using O(107) grid points, LES allows us
There is a critical need for a detailed study of
the small-scale physics at the air-water interface,
which is a foundation for the development of
large-scale simulation and prediction tools.
to as “turbulent eddies,” of which the
size spans a wide range of scales. In
our study, we employ two approaches.
The first is direct numerical simulation (DNS), which resolves all eddies
explicitly. The demand on computing
resources is high and in most cases we
are limited to simple, idealized cases at
small scales. Using state-of-the-art computations, typical physical problems that
can be studied using DNS are limited to
wind speeds of one to two meters per
second over a small wavefield of the order of one meter. The DNS are useful for
characterizing the underlying basic statistics, structures, and mechanisms, thus
providing a useful quantitative picture
of the overall dynamics. DNS has been
shown to be a powerful research tool to
elucidate detailed physical mechanisms
in many other turbulent flows (e.g., the
review by Moin and Mahesh, 1998).
1
to study problems with wind speeds of
up to about 10 m/s blowing over a wave
group. Spatially, this simulation could
obtain resolutions of less than one meter horizontally and a few centimeters
vertically. This simulation resolves the
dynamically important flow structures,
while the effects from sub-grid scales are
included using closure models (effective
ones typically are dissipation models of
the Smagorinsky type). With this approach, the observations obtained using
DNS and LES are consistent, elucidating
the salient features of the air-water interactions. Because the DNS results show
more of the finer-scale details, we focus
below on the discussion based on our
DNS simulations.
In addition to the multi-scale nature
of turbulence, other great challenges in
simulating air-sea coupled turbulent
flows include the large difference in the
physical properties of air and water, and
the complexity associated with free-surface motions, especially with waves. The
density of water is three orders of magnitude larger than that of air, and the
water kinematic viscosity is one order
of magnitude smaller than that for air1.
Because of such disparity, the interaction
between air and water possesses many
unique features not seen in other twophase fluid flows. In our simulations, the
air and water motions interact with each
other through the kinematic and dynamic free-surface boundary conditions at
the air-water interface. The former states
that a fluid particle at the interface stays
on the interface, while the latter specifies
the balance of forces across the air-water
interface. These two boundary conditions are coupled though a novel alternating scheme. Details of our numerical
method can be found in Liu (2005). The
effects of surface waves for these flows
are captured in the simulations. Depending on the sea state (or wave steepness),
a number of treatments are developed:
(1) at low wind speeds when the surface
is almost flat, a fixed-grid approach with
the option of linearized boundary conditions for free-surface deformations,
(2) at moderate wind speeds, a boundLian Shen (lshen@mit.edu) is Assistant
Professor, Department of Civil Engineering,
Johns Hopkins University, Baltimore, MD,
USA. Dick K.P. Yue is Associate Dean of
Engineering and Professor of Hydrodynamics and Ocean Engineering, Department of
Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
The kinematic viscosity (=dynamic viscosity/density) of water is smaller than for air (by a factor of 10) because the density of water is about one thousand times greater than for air. From a
fluid mechanics point of view, a fluid’s kinematic viscosity is often the better way to view things. Heuristically, if dynamic viscosity is associated with the actual stress, then in terms of understanding the kinematics (e.g., velocity changes), what matters is not the magnitude of the stress, but the magnitude of the stress relative to the density of the fluid.
54
Oceanography
Vol. 19, No. 1, Mar. 2006
ary-interface-tracking method that directly captures wave-turbulence interactions with high accuracy, and (3) at high
wind speeds as the waves steepen and
break, an Eulerian-interface-capturing
method based on the level set approach
for the air-water mixed flow. A typical
result using approach 2 is shown in Fig-
ure 1a. For moderate to high wave amplitude and steepness, the wave effects play
an essential role in the air-sea interaction
and must be accounted for. On the other
hand, for small wave magnitudes typical
under low-wind conditions, our extensive
study shows that the presence of waves
has a relatively minor effect on the overall
flow dynamics (see, for example, Shen et
al., 1999), while the surface roughness itself can be obtained from the underlying
pressure field. In this article, we focus on
relatively low wind speed when the waves
are small. Accordingly, the results below
are obtained using approach 1. The situation involving higher wind speeds and
Figure 1. (a) A typical simulation result of air and water motions in the presence of moderate waves. Plotted are contours of streamwise (defined as the direction of wave propagation) velocity normalized by the phase velocity of the
dominant wave. (b) Schematics of coupled air-water Couette
flow. The flow domain, with bottom half water and the top
half air, is set in motion by the constant horizontal motion of
the top boundary of the air. The top and bottom walls represent far-field conditions but not actual physical objects.
Oceanography
Vol. 19, No. 1, Mar. 2006
55
STATISTICS OF ATMOSPHERIC
AND O CEAN FLOWS 
A FIR ST LO OK
large-amplitude waves is discussed in the
last section.
Using systematic simulations on
high-performance parallel computers
with finely resolved temporal and spatial detail, we obtain a complete physical
description of the turbulent air-sea flow
field that fully captures air-water dynamics. This description provides a basis
for the identification of key transport
processes within the atmosphere-ocean
boundary layer. Our objectives are to assess the key processes at the air-sea interface and to establish a physical foundation for the characterization and parameterization of the mass, momentum, and
energy transfer between the atmosphere
and oceans at small scales.
As an example problem that contains all
the key features of low-speed air-sea couple flow, we study the turbulent air-water Couette flow shown in Figure 1b. A
controlling parameter for this problem is
the Reynolds number based on the shear
velocity at the interface, domain halfheight, and kinematic viscosity of the
fluids. For the case shown, this Reynolds
number is 120 for the waterside motion
and 270 for the airside motion. By examining the detailed flow characteristics
at the air-water interface located in the
middle of the domain, we obtain useful
insights into the physics of interfacial
interactions representative of the coupled air-sea turbulent boundary layers.
Of particular interest is to compare and
contrast the physics and features near the
air-water interface to those in classical
boundary layers over a fixed solid wall, a
subject that has been studied extensively
for over a century.
The mean velocity profiles for the air
and water turbulent motions for a representative case are plotted in Figure 2.
Here and hereafter, unless otherwise
pointed out, all the quantities are normalized by domain half-height and the
air velocity at the top boundary. The
stress balance across the air-water interface requires the product of dynamic
viscosity and velocity gradient to be the
Global Coordinates
1
Local Coordinates
0.5
(u+INT - u+)W
(u+ - u+INT)a
u+ = h+
u+ = 2.5lnh+ + 5.0
u+ = 2.5lnh+ + 3.0
15
0
0
Water
Air
u+
Z
20
Water
Z
10
-0.5
-0.5
5
-1
0
0.25
0.5
0.75
1
<u>
-1
0
0.01
<u>
0.02
0
10-1
100
h+
101
102
Figure 2. Left and middle: Air and water mean velocity profiles in global coordinates. Right: Variation of mean velocity near the air-water interface in local
coordinates. In global coordinates, the quantities are normalized by domain half-height and the air velocity at the top boundary. In local coordinates, the
velocity is normalized by friction velocity at the interface, and the distance from the interface is expressed in terms of a wall unit. Shown are the shear flow
in the air and water and the comparison with the boundary layer theory. Triangles and squares are the results obtained from our study. The dashed curves
are predictions by the linear law and the log law.
56
Oceanography
Vol. 19, No. 1, Mar. 2006
same at the two sides of the interface.
Because the value of dynamic viscosity in water is significantly (63.7 times
at 1 atm and 20°C) larger than that in
air, the velocity gradient in the water is
much smaller than that in the air. This is
consistent with our experience that the
wind speed is much larger than the water
current velocity in the ocean. The middle
figure in Figure 2 shows an enlarged
velocity profile in water. It appears that
the velocity variation near the air-water
interface is similar to that near the solid
(top and bottom) wall boundaries. To
further investigate the near-interface behavior, the right figure in Figure 2 compares the velocity profiles in local coordinates. That is, all the physical quantities
are expressed by “wall units” based on
the shear stress at the interface and fluid
density, so that universal physical laws
can be studied. It is seen that, very close
to the interface, the mean velocities of
both air and water are linear functions
of the distances from the interface, while
some distance away the velocities and
distances satisfy a logarithmic law. This
is the same as what we know happens in
wall boundary layers. This resemblance
is much more so on the airside (i.e., to
the first order, the air-water interface behaves like a solid wall to air motions).
For the waterside, however, close examination shows that the viscous sublayer is thinner than that on the airside.
The surface-layer structure can be seen
(a)
1
0
(b)
0. 02
0. 04
0. 06
0. 08
0. 1
1
Air
Air
z
0
0
Water
Water
-0.5
-0.5
-1
Figure 3. Profiles of (a) velocity and
(b) vorticity fluctuations in the air
and water. The solid lines are for
the streamwise (x) components,
the dash-dotted lines for the transverse (y) components, and the
dash-dot-dotted lines for the vertical (z) components. A substantial
difference exists at the interface
(z = 0) between the air and water
sides. The airside variation at the
interface is similar to that at a solid
wall, which is present at the top
boundary (z = 1), while the waterside variation at the interface possesses features significantly different from those near the solid wall
located at z = -1.
0. 5
0. 5
z
from the velocity profile in local coordinates. As shown in Figure 2, a linear
law is valid close to the interface and a
log law is valid away from the interface.
In the semi-logarithm plot, the log law
is represented by a straight line, which
intersects with the velocity axis. This
intersection point is lower in the water
case than that in the air case (5.0 verses
3.0), which indicates that viscous sublayer region is smaller on the waterside.
What causes the reduction in sublayer
thickness in water? This, as it turns out,
can be explained by the different restriction mechanisms of the interface on
turbulence fluctuations. As shown in
Figure 3, on the airside all the three velocity components diminish at the inter-
0
0. 001
0. 002
0. 003
u i, rms
0. 004
0. 005
-1
0
0. 1
0. 2
ω i, rms
0. 3
0. 4
0. 5
Oceanography
Vol. 19, No. 1, Mar. 2006
57
face. This is because the density of air is
much less than that of water, and the air
barely moves the water at the interface
with the shear stress, so the interface
acts more like a solid wall to the air motion. On the waterside, however, only
the vertical velocity is reduced towards
the interface. The water at the interface
has much more freedom for horizontal motion relative to the case of a solid
wall. Consequently, on the waterside, the
viscous sublayer—where the turbulence
transport is dominated by viscous diffusion—is much thinner in this case.
of the velocity gradient. This iso-surface
has a strong correlation with the pressure minimum existing at the vortex
core in high Reynolds flows, and it has
been found to give a clear vortical indication for various types of turbulent
flows. With this vortex definition, we
find that vortical structures in the water
near the interface can be characterized
into mainly three categories: hairpin
vortices, quasi-streamwise vortices, and
interface-attached vortices. Representative vortices of these three types are il-
and Moin, 1988), has been found to be
effective for turbulence-structure statistics. It is essentially a conditional averaging technique. For a specific flow
structure, based on the instantaneous,
three-dimensional flow field obtained
from the simulations, we first use its
key characteristics to identify the events
when such structure appears. For each
event, we isolate the flow field surrounding the structure being studied and then
perform statistical averaging of these
events. After a large number of ensemble
lustrated in Figure 4a.
COHERENT VORTICAL
STRUCTURE S NEAR THE
AIRSEA INTERFACE
USE OF ADVANCED
STATISTICAL TO OL S TO
QUANTIF Y FLOW STRUCTURE S
Vorticity is a measure of the angular
motion of the flow. Coherent vortical structures are found to play an important role in turbulence transport
processes (Robinson, 1991). A great
advantage of simulation-based study is
that it can provide whole-field (spatial
and temporal) data for all the physical
quantities computed. In this case, the
computed three-dimensional vortical
structures and their evolution can be
identified. Figure 4a illustrates the typical vortical structures obtained from
our simulation. The vorticity field in
turbulence is usually complicated, and
various techniques have been developed
for an efficient representation of vortical structures. In our study, we employ
the method developed by Jeong and
Hussain (1995), in which the vortices
are represented by the iso-surface of the
second largest eigenvalue of the tensor
S 2 + 2, with S = (∂ui /∂xj + ∂uj /∂xi) and
= (∂ui /∂xj - ∂uj /∂xi) are respectively
the symmetric and anti-symmetric parts
As shown in Figure 4a, the instantaneous
vortices in the turbulence field are rather
complicated. Due to the chaotic nature
of turbulence, a specific flow structure is
generally not repeated in time or space.
Furthermore, because of the fluctuations in the flow, a flow structure does
not appear in a smooth, well-defined
form. Rather, coherent structures emerge
sharing key common features of the
specific type of the structure in question, together with (smaller) distortions
caused by turbulence noise. Although
results like Figure 4a give us a qualitative
description, for quantified results, other
research tools are called for.
To quantify the effects of vortical
structures, we employ a variable-interval
space-averaging (VISA) technique (Kim,
1983), which is from the variable-interval
time-averaging (VITA) method for laboratory experiments (Blackwelder and Kaplan, 1976). The VISA method, together
with some other methods such as the
stochastic estimation approach (Adrian
averaging, we obtain converged statistics.
Our experience shows that O(103) events
are usually needed. The details for the
implementation of the VISA method are
given in Shen and Yue (2001).
For the VISA statistics of air-sea turbulent coupled flows, the key to its success is the proper characterization of
each flow structure so that when such
structures appear in the flow field, they
can be captured exclusively. For the three
vortical structures shown in Figure 4a,
we use, respectively, large streamwise
vorticity component, ωx, to characterize
quasi-streamwise vortices; large positive
transverse vorticity, ωy, which corresponds to their head portion, to capture
hairpin vortices; and large vertical vorticity, ωz, which indicates the appearance of interface-connected vortices, to
identify interface-attached vortices. We
also use large magnitudes of the surface
divergence, ∂u/∂x + ∂v/∂y, to identify
upwellings and downwellings near the
air-sea interface.
Figure 4b shows an example of the
conditionally averaged results for hairpin vortex structures. Compared to the
instantaneous vortex shown in Figure 4a,
it is clear that the VISA method faithfully
58
Oceanography
Vol. 19, No. 1, Mar. 2006
Z
Y
X
(a)
Air
Interface
Scalar
Concentration
Water
Interface-attached Vortex
Quasi-streamwise Vortex
Z
Hairpin Vortex
Y
X
Interface-attached Vortex
Quasi-streamwise Vortex
Figure 4. (a) Instantaneous vortical structures
in the air and water turbulent flows and instantaneous scalar concentration distributions are
shown. Vortices are represented by the second
largest eigenvalues of the vorticity-strain tensor.
Plotted are three categories of representative
vortical structures: hairpin vortices, quasistreamwise vortices, and interface-connected
vortices. The hairpin vortex is positioned in
such a way that the vorticity in the hairpin
head points in the positive y direction. The
quasi-streamwise and interface-connected
vortices can rotate either way. (b) Coherent
hairpin-shaped vortex structure captured with
the conditional-averaging technique. Plotted is
the conditionally averaged result of about 3000
instantaneous hairpin vortices.
captures the hairpin vortices and produces high-quality flow-field statistics for the
quantitative study of turbulence structures. These results establish a basis for
the mechanistic investigation of air-sea
interaction dynamics. For example, Figure 5 shows the VISA results on a vertical
cross-section of quasi-streamwise vorti-
Z
Air
(b)
Interface
Water
ces pointing in the -x direction. The contours of the streamwise vorticity component and vortex-induced velocity vectors
are plotted in the left figure of Figure 5. It
is shown that on the waterside, due to the
induction of the vortex, the fluids to the
left of the vortex are advected towards
the interface and the fluids on the right
are swept down. Because of this vortexinduced advection, transport of species
near the interface is significantly affected.
The right figure of Figure 5 shows the
contours of concentration fluctuation for
a passive scalar. In this study, the mean
concentration value of the scalar is set
initially to increase upwards. As shown
Oceanography
Vol. 19, No. 1, Mar. 2006
59
Figure 5. Conditionally averaged results of quasi-streamwise vortices
based on about 3000 instantaneous
events are shown. The top figure is a
quasi-streamwise vortex on the waterside. Plotted are contours of streamwise vorticity component ωx and
fluctuation velocity vectors (v , w )
on a vertical (y, z) cross section that
is located at the center of the quasistreamwise vortex. The waterside
vortex induces a mirror vortex of the
opposite sign on the air side. Between
the air-water interface and the mirror
vortex, there exists a micro low-level
jet. The vortices and jet have a significant effect on passive scalar transport
near the interface. The bottom figure
shows contours of scalar concentration fluctuations.
in the figure, the vortex makes the scalar
boundary layer in the left-hand-side upwelling region much thinner. As a result,
transfer of the scalar across the interface
is greatly enhanced there.
An important discovery from our
study is the airside micro low-level jets
60
Oceanography
Vol. 19, No. 1, Mar. 2006
that are induced by the water motions
underneath. A typical example is shown
in the VISA results of waterside upwelling motions plotted in Figure 6. As water
is advected towards the interface during
an upwelling, diverging flow is induced
at the interface. Due to the continuity of
velocity at the interface, diverging flow
must also be present on the airside. Because the shear stress across the interface
needs to be balanced, and because the
value of dynamic viscosity of air is substantially smaller than that of water, the
velocity gradient on the airside is much
larger than that on the waterside. As a result, on the airside, a jet flow in the vicinity of the interface is formed, as shown in
Figure 6. Such a mechanism is also present in the case of quasi-streamwise waterside vortices. As shown in Figure 5, the
negative streamwise vortex in the water
induces a positive mirror vortex in the air
above, as expected. What is interesting is
that because of the micro low-level jet, a
large vorticity of the opposite sign of the
mirror vortex is formed on the airside
between the induced mirror vortex and
the interface. Through simulations such
as these, we find that the micro low-level
jet is a salient feature in air-water coupled flows and that it plays an important
role in air-sea interaction dynamics.
USING FLOW STRUCTURE
INFORMATION TO IMPROVE
UNDER STANDING OF FLOW
STATISTICS
The knowledge of flow structures in airsea interactions provides a basis for better understanding of flow turbulent statistics. As an example, we show the analysis of turbulent kinetic energy (TKE).
TKE is defined as
, with the
fluctuations of velocity components.
TKE is an important measure of the
magnitude of turbulence in atmosphere
and ocean flows, and modeling the TKE
budget is critical to improved understanding and prediction of coupled atmosphere-sea turbulent flows. A good
understanding of the evolution of TKE
and its components allows us to develop
further closure models needed, for example, in larger-scale and coarser-grid
simulations such as those used in mesoscale LES and Reynolds-averaged Navier-Stokes (RANS) computations. In
Figure 6. Conditionally averaged results of waterside upwelling based on about 3000 instantaneous events. Upwelling motion on the waterside is shown by contours of surface
divergence (∂u/∂x + ∂v/∂y) and fluctuation velocity vectors (v , w ) on a vertical (y, z)
cross section that is located at the center of the upwelling. Induced by the waterside upwelling, on the airside there exist a downwelling and two micro low-level jets on the edges
of the downwelling. Note that in the figure, both the velocity vector scales and the contour levels of surface divergence are different between the waterside and airside.
this study, it is found that the analysis of
coherent structures provides important
physical insights to the mechanism of
the TKE budget.
The evolution of TKE is governed by
a number of processes. It is produced by
the interaction between Reynolds stress
and the shear in the mean flow. Meanwhile, TKE is dissipated by viscosity. In
addition to these source and sink processes, TKE is transported among different flow regions by pressure fluctuations
and velocity fluctuations. At regions
where the TKE varies abruptly, for exam-
ple, at a boundary layer, viscous diffusion
also contributes to the TKE transport.
Based on the extensive data obtained
from our computer simulations, we are
able to perform detailed quantification and analysis of each process in the
TKE budget. As shown in Figure 7, TKE
production is large near the interface;
viscous diffusion is only significant very
close to the interface and the pressure
transport is much smaller than other
terms. The variation of the turbulent
transport due to velocity fluctuations
and the TKE dissipation is noteworthy.
Oceanography
Vol. 19, No. 1, Mar. 2006
61
Figure 7 shows that velocity fluctuations
transport TKE from the bulk region of
the air to the near-interface region. On
the waterside, turbulence transport removes part of the TKE from the near-interface region and puts it into the deeper
region. Dissipation in the air increases
towards the interface and reaches a maximum at the interface, again behaving
like the boundary layer near a solid wall.
On the waterside, as the interface is approached, dissipation increases first, then
decreases and finally increases again to
reach its maximum value at the interface.
The behaviors of some of the TKE
budget processes are relatively easy to
understand. For example, the production
term is the product of the mean shear
and the Reynolds stress. As the air-water
interface is approached, although the
shear increases, the Reynolds stress decreases rapidly because of the constraint
of vertical motions by the interface. As a
result, production decreases towards the
interface. The variation of the viscous
diffusion and velocity transport terms
is governed by the variation of velocity
fluctuation profiles (Figure 3).
On the other hand, some other processes in the TKE balance are truly complex and they can only be explained
based on our knowledge of the detailed
vortical structures. Energy dissipation
is a typical example. Our study reveals
0.2
Production, Pk
Pressure Diffusion, Πk
Turb. Diffusion, Tk
Viscous Diffusion, Dk
Dissipation, εk
0.1
Air
z 0
Water
that the complicated variation of dissipation (Figure 7) is caused by the unique
vortex-interaction dynamics at the airwater interface (Figures 4 and 5). On the
waterside, as the interface is approached,
the first peak in dissipation is associated
with intense vortical activities near the
interface, as evidenced by the instantaneous vortical structures plotted in Figure 4a and by the vorticity-fluctuation
statistics plotted in Figure 3. Closer to the
interface, horizontal vortices diminish
within the surface layer. This phenomenon is similar to what we found in the
free-surface turbulence case (without
the air above the interface; Shen et al.,
1999), where TKE dissipation is reduced
and reaches a local minimum near the
surface. The present case of coupled airwater flow is, however, different from the
problem of free-surface turbulence in
that air motions cause stress fluctuations
at the interface. As a result, vorticity fluctuations and the associated TKE dissipation both reach their maxima at the interface (Figures 3 and 7). On the airside,
the enhanced dissipation near the air-water interface is caused by the large shear
stress at the interface and the presence of
the micro low-level jets we show earlier.
Such information is important for the
development of turbulence modeling for
the coupled air-water boundary layers.
-0.1
FUTURE RE SEARCH
DIRECTIONS
-0.4
-0.2
0
0.2
0.4
Figure 7. Processes affecting the turbulent kinetic energy (TKE) budget near the
air-water interface. Shown are TKE production, dissipation, transport due to
pressure fluctuation and velocity fluctuation, and viscous diffusion. All the quantities are normalized by the friction velocity at the interface and the kinematic
viscosity of air and water in the corresponding regimes.
62
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Vol. 19, No. 1, Mar. 2006
In this study we use direct simulations to
investigate the small-scale coupling dynamics of air and water turbulent flows
near an air-sea interface. Through systematic high-resolution simulations, we
obtain a detailed description of the velocity and vorticity fields in the coupled
air-water turbulent flow. These data sets
provide us with a physical basis to obtain
high-quality flow statistics and structures.
The coherent vortical structures identified in this study are found to play an important role in the near-interface transport process. Using advanced statistical
tools, we are able to quantify the characteristics of those vortical structures,
which in turn help us better understand
and model turbulence statistics such as
the TKE budget in air-sea interactions.
The physical insights obtained from
this study are important for the development of turbulence modeling and
prediction tools for air-sea interactions.
We are now actively pursuing two fronts
of research. First, we are performing a
comparison with field data, in particular
the data collected at the Martha’s Vineyard Coastal Observatory and Air-Sea
Interaction Tower during the CBLAST
experiment (more information available at http://www.whoi.edu/science/
AOPE/dept/CBLASTmain.html), which
include wind and momentum flux profiles measured from the meteorological
mask and the air-sea interaction tower
(ASIT), current and wave characteristics
from the ASIT, and the directional wave
spectra from the offshore seanode. Our
numerical simulation can be used as a
powerful tool to help interpretation and
syntheses of field data. For example, the
TKE budget obtained from our study is
valuable to the parameterization for airocean momentum and kinetic energy
vertical transfer.
The ultimate objective is to obtain
multi-scale simulation capabilities that
link the finely resolved turbulent flow
simulations above with truly large-scale
gravity wavefield predictions. The ob-
jective is to bridge the gap between the
parameterization of small-scale air-seawave interaction physics and high-resolution regional-scale modeling of ocean
waves. For the latter, our recent focus
has been on developing numerical capability for the direct, phased-resolved
simulation of nonlinear ocean waves for
a field evolving over a distance of up to
hundreds of kilometers. The key difference for these simulations is that they
are based on potential-flow formulation.
Computationally, potential-flow simulations can be several orders of magnitude
more efficient that DNS and LES. One
of the reasons for this efficiency is that
potential-flow solutions generally require discretization of the boundary of
the domain (which is two dimensional)
versus the three-dimensional volume
discretization needed for viscous/turbulent flows. In potential flow-wave simulations, viscous and turbulence effects
important in phenomena such as wavebreaking dissipation and wind forcing
are modeled indirectly. As it turns out,
the key to success with these models lies
in the types of DNS and LES turbulence
simulations discussed earlier. The success of the multi-scale approach depends
on our ability to integrate faithfully the
effects of small-scale processes of windenergy supply and wave-breaking dissipation on large-scale nonlinear wave
evolutions. This approach builds on two
advancements made recently: the numerical tools for direct phase-resolved
simulation of a large-scale wave field developed at the Massachusetts Institute of
Technology, and the high-performance
numerical capabilities for atmosphereocean-wave interactions at small scales
obtained at the Johns Hopkins Univer-
sity (and the substantial physical understanding obtained based on simulation
results). After completion, we will be capable of predicting deterministically the
evolution of a large-scale (O(103~4km2))
nonlinear ocean wave-field in realistic
marine environments with the presence
of high winds and whitecapping.
ACKNOWLED GEMENTS
This research is financially supported
by the CBLAST project of the Office of
Naval Research (ONR) with a portion of
the computational resources provided
by ONR through the U.S. Department
of Defense High Performance Computing Modernization Program (HPCMP).
We thank the three reviewers for their
comments.
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